EQUAL-AREA RULE METHODS FOR TERNARY-SYSTEMS

Eubank and Hall have recently shown the equal area rule (EAR) applies to the composition derivative of the Gibbs energy of a binary system a t fixed pressure and temperature regardless of derivative continuity. A sufficient condition for equilibria, EAR is faster and simpler than either the familiar tangent-line method or the area method of Eubank e t al. Here, we show that EAR can be extended to ternary systems exhibi ting one, two, or three phases at equilibrium. A single directional ve ctor is searched in composition space; at equilibrium, this vector is the familiar tie line. A sensitive criterion for equilibrium under EAR is equality of orthogonal derivatives such as (partial derivative g/p artial derivative x(1))(x2P,T) at the end points (alpha and beta), whe re g = (Delta(m)G/RT). Repeated use of the binary algorithm published in the first reference allows rapid, simple solution of ternary proble ms, even with hand-held calculators for cases where the background mod el is simple (e.g., activity coefficient models) and the derivative co ntinuous.